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Simple continued fraction
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==References== * {{cite journal |last1= Bunder |first1= Martin W. |last2= Tonien |first2= Joseph |year=2017 |title=Closed form expressions for two harmonic continued fractions |journal=The Mathematical Gazette |volume=101 |issue=552 |pages= 439–448 |url=https://ro.uow.edu.au/cgi/viewcontent.cgi?article=1781&context=eispapers1 |doi=10.1017/mag.2017.125 |s2cid= 125489697 }} * {{cite journal |last1= Chen |first1= Chen-Fan |last2= Shieh |first2= Leang-San |year= 1969 |title= Continued fraction inversion by Routh's Algorithm |journal= IEEE Trans. Circuit Theory |volume= 16 |number= 2 |pages= 197–202 |doi= 10.1109/TCT.1969.1082925 }} * {{cite journal |last= Collins |first= Darren C. |date= 2001 |title= Continued Fractions |journal= MIT Undergraduate Journal of Mathematics |url= http://www-math.mit.edu/phase2/UJM/vol1/COLLIN~1.PDF |url-status= dead |archive-url= https://web.archive.org/web/20011120064343/http://www-math.mit.edu/phase2/UJM/vol1/COLLIN~1.PDF |archive-date= 2001-11-20 }} * {{cite book |last1= Cuyt |first1= A. |last2= Brevik Petersen |first2= V. |last3= Verdonk |first3= B. |last4= Waadeland |first4= H. |last5= Jones |first5= W. B. |year= 2008 |title= Handbook of Continued fractions for Special functions |publisher= Springer Verlag |isbn= 978-1-4020-6948-2 }} * {{cite web |author=Encyclopædia Britannica |title= Continued fraction – mathematics |date= 2013 |url= https://www.britannica.com/science/continued-fraction |access-date= 26 April 2022 |ref={{harvid|Encyclopaedia Britannica|2013}} }} * {{cite web |last= Euler |first= Leonhard |date= 1748 |title=E101 – Introductio in analysin infinitorum, volume 1 |url= https://scholarlycommons.pacific.edu/euler-works/101/ |publisher= The Euler Archive |access-date= 26 April 2022 }} * {{Cite web |last= Foster |first= Tony |date= 22 June 2015 |url= https://www.theoremoftheday.org/NumberTheory/EulerCF/TotDEulerCF.pdf |archive-url=https://web.archive.org/web/20131211085948/http://theoremoftheday.org/NumberTheory/EulerCF/TotDEulerCF.pdf |archive-date=2013-12-11 |url-status=live |title= Theorem of the Day: Theorem no. 203 |publisher= Robin Whitty |access-date= 26 April 2022 }} * {{cite journal |last= Gragg |first= William B. |year= 1974 |title= Matrix interpretations and applications of the continued fraction algorithm |journal= Rocky Mountain J. Math. |volume= 4 |number= 2 |doi= 10.1216/RMJ-1974-4-2-213 |page= 213 |s2cid= 121378061 |doi-access= free }} * {{Cite book |last1= Hardy |first1= Godfrey H. |last2= Wright |first2= Edward M. |date= December 2008 |orig-date= 1979 |title= An Introduction to the Theory of Numbers |publisher= Oxford University Press |edition= 6 |isbn= 9780199219865 }} * {{cite journal |last= Heilermann |first= J. B. H. |year= 1846 |title= Ueber die Verwandlung von Reihen in Kettenbrüche |journal= Journal für die reine und angewandte Mathematik |volume= 33 |pages= 174–188 |url= http://www.digizeitschriften.de/dms/resolveppn/?PID=PPN243919689_0033%7Clog13 }} * {{Cite book |last1= Jones |first1= William B. |last2= Thron |first2= W. J. |year= 1980 |title= Continued Fractions: Analytic Theory and Applications. Encyclopedia of Mathematics and its Applications. |publisher= Addison-Wesley Publishing Company |location= Reading. Massachusetts |volume= 11 |isbn= 0-201-13510-8 |url-access= registration |url= https://archive.org/details/continuedfractio0000jone }} * {{cite book |last= Khinchin |first= A. Ya. |author-link= Aleksandr Khinchin |year= 1964 |title= Continued Fractions |url= https://archive.org/details/continuedfractio00khin_0 |url-access= registration |orig-year= Originally published in Russian, 1935 |publisher= [[University of Chicago Press]] |isbn= 0-486-69630-8 }} * {{cite book |last= Long |first= Calvin T. |date= December 1972 |title= Elementary Introduction to Number Theory |edition= 2nd |publisher= [[D. C. Heath and Company]] |location= Lexington |isbn= 9780669627039 }} * {{cite journal |last= Magnus |first= Arne |year= 1962 |title= Continued fractions associated with the Padé Table |journal= Math. Z. |volume= 78 |pages= 361–374 |doi= 10.1007/BF01195180 |s2cid= 120535167 }} * {{cite book |last1= Niven |first1= Ivan |last2= Zuckerman |first2= Herbert S. |last3= Montgomery |first3= Hugh L. |date= 1991 |title= An introduction to the theory of numbers |url= https://archive.org/details/introductiontoth0000nive |url-access= registration |edition= Fifth |location= New York |publisher= [[John Wiley & Sons|Wiley]] |isbn= 0-471-62546-9 }} * {{cite book |last= Perron |first= Oskar |author-link= Oskar Perron |year= 1950 |title= Die Lehre von den Kettenbrüchen |publisher= Chelsea Publishing Company |place= New York, NY }} * {{cite book |last1= Pettofrezzo |first1= Anthony J. |last2= Byrkit |first2= Donald R. |date= December 1970 |title= Elements of Number Theory |publisher= [[Prentice Hall]] |location= Englewood Cliffs |isbn= 9780132683005 }} * {{cite journal |last = Rieger |first = Georg Johann |year = 1982 |title = A new approach to the real numbers (motivated by continued fractions) |journal = Abhandlungen der Braunschweigischen Wissenschaftlichen Gesellschaft |url=https://publikationsserver.tu-braunschweig.de/servlets/MCRFileNodeServlet/dbbs_derivate_00031201/Rieger_A_new_approach_to_the_real_numbers.pdf |archive-url=https://web.archive.org/web/20201210192036/https://publikationsserver.tu-braunschweig.de/servlets/MCRFileNodeServlet/dbbs_derivate_00031201/Rieger_A_new_approach_to_the_real_numbers.pdf |archive-date=2020-12-10 |url-status=live |volume = 33 |pages = 205–217 }} * {{cite book |last1= Rockett |first1= Andrew M. |last2= Szüsz |first2= Peter |year= 1992 |title= Continued Fractions |url= https://archive.org/details/continuedfractio0000rock |url-access= registration |publisher= World Scientific Press |isbn= 981-02-1047-7 }} * {{cite book |last= Sandifer |first= C. Edward |year= 2006 |title= How Euler Did It |chapter= Chapter 32: Who proved ''e'' is irrational? |publisher= [[Mathematical Association of America]] |pages= 185–190 |isbn= 978-0-88385-563-8 |lccn= 2007927658 |url= http://eulerarchive.maa.org/hedi/HEDI-2006-02.pdf |archive-url=https://web.archive.org/web/20140319071616/http://eulerarchive.maa.org/hedi/HEDI-2006-02.pdf |archive-date=2014-03-19 |url-status=live }} * {{cite journal |last1= Scheinerman |first1= Ed |last2= Pickett |first2= Thomas J. |last3= Coleman |first3= Ann |year=2008 |title=Another Continued Fraction for π |journal= The American Mathematical Monthly |volume=115 |issue=10 |pages= 930–933 |doi= 10.1080/00029890.2008.11920610 |jstor= 27642639 |s2cid= 11914017 }} * {{cite book |last= Shoemake |first= Ken |year= 1995 |editor-last= Paeth |editor-first= Alan W. |title= Graphics Gems V (IBM Version) |chapter=I.4: Rational Approximation |chapter-url= https://books.google.com/books?id=8CGj9_ZlFKoC&pg=PA25 |pages= 25–31 |publisher=Academic Press |location=San Diego, California |isbn= 0-12-543455-3 }} * {{cite journal |last= Siebeck |first= H. |year= 1846 |title= Ueber periodische Kettenbrüche |journal= Journal für die reine und angewandte Mathematik |volume= 33 |pages= 68–70 |url= http://www.digizeitschriften.de/dms/resolveppn/?PID=PPN243919689_0033%7Clog5 }} * {{cite journal |last= Thill |first=M. |year=2008 |title=A more precise rounding algorithm for rational numbers |journal=Computing |volume=82 |issue=2–3 |pages=189–198 |doi=10.1007/s00607-008-0006-7 |s2cid=45166490 }} * {{cite web |last=Thurston |first=Ben |title= Estimating square roots, generalized continued fraction expression for every square root |publisher= The Ben Paul Thurston Blog |date= 2012 |url= http://benpaulthurstonblog.blogspot.com/2012/05/estimating-square-roots.html |access-date= 26 April 2022 }} * {{cite book |last= Wall |first= Hubert Stanley |author-link= Hubert Stanley Wall |year= 1948 |title= Analytic Theory of Continued Fractions |publisher= D. Van Nostrand Company, Inc. |isbn= 0-8284-0207-8 }} * {{cite web |last= Weisstein |first= Eric Wolfgang |author-link= Eric W. Weisstein |date= 2022 |title=Periodic Continued Fraction |editor= MathWorld |url=https://mathworld.wolfram.com/PeriodicContinuedFraction.html |access-date= 26 April 2022 }}
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